How do you write the polar equation #theta=pi/3# in rectangular form?

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Answer 1 · 2016-11-08T20:21:24

Please see the explanation for steps leading to the equation:
#y = (tan^-1(pi/3))x#

Substitute #tan(y/x)# for #theta#

#tan(y/x) = pi/3#

Obtain #y/x# on the left by using the inverse tangent on both sides:

#tan^-1(tan(y/x)) = tan^-1(pi/3)#

#y/x = tan^-1(pi/3)#

Multiply both sides by x:

#y = (tan^-1(pi/3))x#

Answer 2 · 2016-11-09T09:31:33

#y =sqrt3x#

The relation between polar coordinates #(r,theta)# and Cartesian rectangular coordinates #(x,y)# is given by

#x=rcostheta#, #y=rsintheta# and #tantheta=y/x#

As #theta=pi/3#, we have #tantheta=sqrt3#

and equation is

#y/x=sqrt3#

Multiply both sides by #x#

#y =sqrt3x#